Republicans see the bill as a way to fulfill President Obama's own complaint from last year about the "maze" of federal job training programs. Rep. Virginia FoxxVirginia Ann FoxxTaxpayers and consumers alike should cheer defeat of the farm bill A call to service without debt Congress, pass the PROSPER Act for federal student aid reform MORE (R-N.C.) noted Obama's past complaint during debate, and said the House should pass the bill to help advance his goal.

Foxx also noted that the Government Accountability Office (GAO) found several dozen federal jobs programs that are duplicative, and that most of them have not been audited.

"Today, many un- and underemployed Americans have turned to federal workforce education programs to develop the skills they need to be competitive for jobs," she said. "But instead of an easy-to-navigate responsive system, many have found a complex bureaucracy unresponsive to their needs and concerns."

Rep. Luke Messer (R-Ind.) added that while 12 million Americans are looking for work, there are 3.6 million available jobs that are not filled because the federal programs are not adequately training people.

Democrats opposed the bill broadly as something that would end up hurting people who benefit from these programs. Democrats walked out of a House Education and the Workforce Committee markup of the bill last week in protest.

But that action allowed Republicans to dismiss Democratic complaints that the GOP was ignoring the minority. In response to complaints that the bill is not being moved along via "regular order," Foxx argued that it was Democrats who left the committee markup last week.

Passage of the rule means the House will debate the bill Friday, and then consider five amendments before passing it.